As simple as can be:
- Basically - a lot of notes doesn't necessarily mean 'fast' tempo.
- The 'Time-signature' is just the indicator for the basic 'pulse' of your song not for the speed of the melody or any other element!
- The 'Tempo' of this basic beat is by default measured in quarter-notes - BPM.
- Traditionally the 'time-signature' is also measured and indicated in quarter-notes (common-time).
- When it comes to 'smaller' signatures (n/8) we want to indicate a different perception of the basic pulse, although we tend to group these eights back together (when we e.g. raise the tempo) just to fit into our basic perception of a basic '(quarter-note)-pulse' -> (e.g. 6/8 into 2 groups of 3 eights)
4/8 has - you already guessed it - the same tempo as 2/4:
As BPM counts the beats in quarter-notes you have to bring both signatures onto the same level in order to be able to compare their 'tempo'.
Now, they are - 4/4 vs. 2/4 - so 'SAME' Tempo - one beat per second at 60 BPM.
But - you just might wanna express your intent to play the tune more 'agitato' and fast (double time) and even write out all the quarter notes as eights. The Tempo (bpm) would stay the same! You are just playing in double time. And of course you could - additionally - indicate this by using a n/8 signature!
e.g. you could use a 8/8 instead of a 4/4 - same Tempo - but you convey another feeling of the basic pulse of your song!
If you want the reversed effect you would write an 'alla breve' signature or 2/2 or 4/2.
The time-signature essentially indicates the basic 'PULSE' of your composition that e.g. a conductor is most likely to convey to the orchestra. Your foot is your conductor and shows that intent to your body ;-) and this should also be reflected in your score.
If you want to have the basic beat of the BPM signature (quarter by default) understood differently you have to explicitly write e.g.
- [symbol of an eighth-note] = 60 BPM
- [symbol of a dotted quarter-note] = 60 BPM
For example if you had this already mentioned 6/8 and you wanted the pulse to beat two times per measure/bar (3 eights) and last exactly for one second - almost like triplets in a common-time...
A Viennese Waltz, although giving a very clear message of a 3/4 quarter-note pulse, has a very strong impulse on the 1st beat, and a conductor will most likely convey this to the orchestra by beating once on every bar. But as soon as a ritardando comes along he will definitely go back to 3 beats.
So Tempo-signature, Time-signature and other annotations by the composer always go together to convey a good understanding of the intended tempo, pulse and feeling of the composition!
When headed to some destination you can make a lot of small but fast steps or a few slow but big steps. Although your body would convey a totally different message to someone looking at your (stressed, relaxed or whatever) gestures - you would reach your destination at the same time...